certitud, certeza o exactitud vs. precisión nitidez o ... · vs. precisión, nitidez o...

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

1

Accuracy versus Precision: the target analogy

Certitud, certeza o exactitud

vs. Precisión, nitidez o repetitividad


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small statistical

uncertainity

true value

large statistical

uncertainity

average value

Individual observations

outlier

systematic error

Precise but inaccurate measurement

Imprecise but accurate measurement

statistical error

outlier

(a) (b)

Data points with (a) low precision and (b) high precision

(a) Has some average “accuracy” but (b) has low accuracy

Accuracy versus precision: the target analogy Certitud, certeza o exactitud vs. precisión (nitidez, repetibilidad)

Dispersion vs. Concentration 3 Jorge Márquez - Instrumentación & Señales - UNAM 2012

target = true value

Data points with (a) low accuracy and (b) high accuracy.

(both (a) and (b) have average high precision)

(a) (b)

4 Jorge Márquez - Instrumentación & Señales - UNAM 2012

(a) Very low accuracy and very low precision

(b) Very high accuracy and “very high” precision with

two outliers (datos intrusos)


(a) “Anisotropic” precision and “medium” average accuracy

(b) Low accuracy (best shot at “8”), but precision is ill-defined

(two populations of “high precision”???)


Imprecise, vague:

Somebody threw something somewhere before the fire.

Highly precise, detailed (but some irrelevant details):

A caucasic teenager, black-jet haired and dressed in

fuchsia, threw a 35 cm burning log in the east border of

the forest of Winsburg, 15 minutes before the fire was

discovered by Mr. Henry Potter Jr.

¿Is it accurate?

Relatively precise but innacurate (false and inconsistent):

Benganim Frankylinn invented the chiles rellenos in

Mars 1971, during the 296 anniversary of the Mexican

battle of the 6 of may against the Germans in 1784.



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A scientific abstract should contain useful and precise information such as:

Abstract: We measured the endocardial convective heat transfer coefficient, h, at 22 locations in the cardiac chambers of 15 pigs in vivo. A thin film Pt catheter tip sensor in a Wheatstone-bridge circuit, similar to a hot wire/film anemometer, measured h. Using fluoroscopy, we could precisely locate the steerable catheter sensor tip and sensor orientation in pigs’ cardiac chambers. With flows, h varies from 2500 to 9500 W/m2·K. With zero flow, h is approximately 2400 W/m2·K. These values of h can be used for the FEM modeling of radiofrequency cardiac catheter ablation.

Compare that with an abstract that contains little, imprecise information:

Abstract: This paper describes how to measure the convective heat transfer coefficient in pigs. It describes how to make the probe, how to calibrate it, precautions to take when making measurements in the pig. It also describes the circuit and equations that assist in interpreting the results. It gives references for further study.

Accuracy and precision in terms of a distribution of observations (not necessarily a Gaussian); the final measure is the mean of N observations.

With regard to accuracy we can distinguish:

• The difference between the mean of the measurements and the reference value, the bias. Establishing and correcting for bias is necessary for calibration.

• The combined effect of bias and precision (=spread, ~2sigma in a Gaussian).


1

1N

nnN

x x

2

1

1

– 1( – )

N

nnNx x x

x

//upload.wikimedia.org/wikipedia/commons/3/38/Accuracy_and_precision.svg

Precision is often stratified into:

Repeatability — the variation arising when all efforts are

made to keep conditions constant by using the same

instrument and operator, and repeating during a short time

period; and,

Reproducibility — the variation arising using the same

measurement process among different instruments and

operators, and over longer time periods


Precision is given as a standard deviation


- UNAM 2012

11 diagram


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ISO 5725 Standard (Norma) 2008

Accuracy Determination

Accuracy (Exactitud)

Precision (Precisión)

Trueness (Veracidad)

Bias

(Sesgo) Reproducibility (Reproducibilidad)

Repeatability (Repetibilidad)


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Absolute Error

errabs = xi xtrue

Random Error

errrand = xi x

Systematic Error

errsys= x xtrue

ISO 5725-6 Quality Control

Evaluated by the standard deviation {xi} Precision

Accuracy

Trueness

+


- UNAM 2012 14

Up to date (2013), no accurate definition of accuracy

… since noise (dispersion) may increase precision

(as the significant number of digits resolution)!

…and accuracy (as in an average)

… and no precise definition of precision…

n measurements

X X X X X X X X X

Signal + 0 noise = 0

X X X

X

X

X

X X

X

+ high 0-mean noise >> 1

AV

ER

AG

E

AV

ER

AG

E

X

X

X

*Higher Precision … with noise

X X X X

X

X X

X

X

+ supra-resolution noise ≈ 1

AV

ER

AG

E

X

X X X X

X X

X X

X

+ sub-resolution noise < 1

AV

ER

AG

E

X

X X

X X

X

i samples

Sub-sampling noise

*Beyond Nyquist … with grid noise

X

X X

X

X X

X

X

X

X

X

X

X

X

X

X

X

X

X

X X

X

X X

X

X

X

X

X

X

X

X

X

X

X

X

Super-resolution

feature size:

feature size:

Jorge Márquez - Instrumentación

& Señales - UNAM 2012

17

Superresolución Morfológica por Nanoposicionamiento en Imágenes de Microscopia Optica

Jorge Márquez y Naser Qureshi

Objetivo: Aumentar resolución de imágenes de microscopia mediante adquisiciones con

diferencias de posición sub-pixel (precisión 0.5 nm. Aplicaciones Biomédicas en 2014:

análisis de conexiones de micronúcleos celulares en estudios en citotoxicología y

restauración/estudio de la textura de preparaciones inmunohistocitológicas.

N adquisiciones con variaciones subpixel Restauración a resolución factor N


- UNAM 2012 18

X X X X

X

X X

X

X

+ supra-resolution noise ≈ 1

AV

ER

AG

E

X

X X X X

X X

X X

X

+ sub-resolution noise < 1

AV

ER

AG

E

X

X X

X

X

X

X Under some conditions

a high dispersion gives

“better precision” of an

average than a low

dispersion.

Better than this !

Output

Input

Output

Input

(a) (b)

(a) The one-point calibration may miss nonlinearity.

(b) The two-point calibration may also miss nonlinearity.


1

1N

nnN

x x

Dark blue is less than one standard deviation from the mean. For the

normal distribution, this accounts for about 68% of the set, while two

standard deviations from the mean (medium and dark blue) account

for about 95%, and three standard deviations (light, medium, and

dark blue) account for about 99.7%


2

1

1

–1( – )

N

nnN

x x

certitud, certeza o exactitud vs. precisión nitidez o ... · vs. precisión, nitidez o...

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